The joint distribution of the Parisian ruin time and the number of claims until Parisian ruin in the classical risk model

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• 作者：Irmina Czarna^a ; ^{czarna@math.uni.wroc.pl" class="auth_mail" title="E-mail the corresponding author} ; Yanhong Li^b ; ^{yanhonglink@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Zbigniew Palmowski^c ; ^{zbigniew.palmowski@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Chunming Zhao^d ; ^{cmzhao@swjtu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Classical risk model ; Number of claims ; Parisian ruin ; Mixed Erlang
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：499-514
• 全文大小：1915 K

文摘

In this paper we propose new iterative algorithm of calculating the joint distribution of the Parisian ruin time and the number of claims until Parisian ruin for the classical risk model. Examples are provided when the generic claim size is mixed Erlang distributed. We focus on the exponentially and the class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304745&_mathId=si85.gif&_user=111111111&_pii=S0377042716304745&_rdoc=1&_issn=03770427&md5=6c402ea772fa651214c60b11c2f9a921">class="imgLazyJSB inlineImage" height="15" width="82" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716304745-si85.gif">class="mathContainer hidden">class="mathCode">$\mathrm{Erlang}(k,\mu )$ (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304745&_mathId=si86.gif&_user=111111111&_pii=S0377042716304745&_rdoc=1&_issn=03770427&md5=aaf806177b6d1a8971d2c6e3d432707b" title="Click to view the MathML source">k≥2class="mathContainer hidden">class="mathCode">$k\ge 2$) distributed claim sizes.